QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 7×7 logic puzzle

7×7 · sharp · 16 steps

A
B
C
D
E
F
G
1
2
3
4
5
6
7
1
2
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3
4
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5
6
🐱
7
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This 7×7 board rates as sharp (difficulty score 1021). Solving it from scratch takes 25 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, marking D1 would force B5 (the last open cell in row 5), and then row 6 would be left with no open cell for its marker. So D1 can't be the marker there.
  4. After that, every remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, marking B2 would force A4 (the last open cell in region 1), and then region 5 would be left with no open cell for its marker. So B2 can't be the marker there.
  6. From there, if C2 were the marker, it would force B7 (the last open cell in column B), then A5 (the last open cell in region 5), then D6 (the last open cell in region 6), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  7. Following that, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  8. First, every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  9. Next, every open cell in row 6 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  10. Then, place a marker at B5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 2 touching neighbours.
  12. Now, place a marker at F4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
  14. Following that, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  15. First, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  16. Finally, place a marker at A2. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎